Question: Simplify the following expression: $a = \dfrac{3k^2 - 9k + 6}{k - 1} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ a =\dfrac{3(k^2 - 3k + 2)}{k - 1} $ Then we factor the remaining polynomial: $k^2 {-3}k + {2} $ ${-1} {-2} = {-3}$ ${-1} \times {-2} = {2}$ $ (k {-1}) (k {-2}) $ This gives us a factored expression: $\dfrac{3(k {-1}) (k {-2})}{k - 1}$ We can divide the numerator and denominator by $(k + 1)$ on condition that $k \neq 1$ Therefore $a = 3(k - 2); k \neq 1$